On the Regularity for Solutions of the Micropolar Fluid Equations

Abstract

-We give sufficient conditions on the kinematics pressure in order to obtain regularity and uniqueness of the weak solutions to the micropolar fluid equations.

A Beale-Kato-Madja Criterion for Magneto-Micropolar Fluid Equations with Partial Viscosity

“…The incompressible magneto-micropolar fluid equation 1.1 has been studied extensively see [1][2][3][4][5][6][7] . In 2 , the authors have proven that a weak solution to 1.1 has fractional time derivatives of any order less than 1/2 in the two-dimensional case.…”

Exponential stability for magneto-micropolar fluids

“…Existence for local and global in time strong solutions was obtained respectively in [24,18]. In [19], the authors treated uniqueness questions for weak solutions. In [25,20], the authors studied local and uniform in time convergence rates for the approximate solutions constructed by the Galerkin method.…”

“…The evolution case was studied in [31] through a semigroup approach (see also [30]). Linearization and successive approximations have been considered in [4,19] to give sufficient conditions on the kinematics pressure in order to obtain regularity and uniqueness of the weak solutions to the micropolar fluid equations. More recently, in [14] the authors considered a weak-L p Prodi-Serrin type regularity criterion.…”

Existence and uniqueness of strong solution for the incompressible micropolar fluid equations in domains of $${\mathbb{R}^3}$$

“…Setting conditions on the pressure in [23] is studied the regularity of solutions. In [22] (see also [17]), Rojas-Medar obtained the convergence rates associated to the approximate solutions constructed by the Galerkin method. The existence of reproductive solution (so called periodic weak solution) for the previous system was proved in [20].…”